HINT: <no title>
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You need to choose variables to represent the things
you want to find and write equations based on the information in the
question.
STEP: Pick variables for the things we want to know
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The two things we want to know in this question are
the prices for each of the items (a pizza and a milkshake). To begin, we
can pick a variable for each of these numbers. It is helpful to pick
variables which remind you about the things in the question:
pm=the price of a pizza=the price of a milkshake
STEP: Write equations based on the information in the question
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Next we need to write equations based on what the
question tells us. In other words, we need to translate the words in the
question into equations.
The first point says that "the total cost for the 7 pizzas and 5 milkshakes is R342."
We can use the expression 7p to represent the price of the 7 pizzas. Similarly, the expression 5m represents the price of the 5 milkshakes.
With these values we can write a full equation for the prices:
In words: In maths: the total cost for the 7 pizzas and 5 milkshakes is R3427p+5m=342
Now we can use the second point. It says, "a pizza costs R6 more than a milkshake." We can write this as an equation like this:
In words: In maths: a pizza costs R6 more than a milkshakep=m+6
STEP: Solve the equations simultaneously
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Now that we have two equations, we need to solve them simultaneously.
7p+5mp=342=m+6
We could use elimination, but substitution is a better choice (because p is already the subject). Substitute the second equation into the first equation and solve!
7p+5m7(m+6)+5m7m+42+5m12mm=342=342=342=342−42=30012=25
This means that the price of one milkshake is R25.
STEP: Find the other variable's value
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Finally, use the value we found for m to find the value of p (the price of a pizza). We can use either equation to do this, but the second one is easier to use (because p is already isolated).
p=m+6=25+6=31
The price for one pizza is R31.
STEP: Write the final answer
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It is important to write the answer to a word problem as a complete sentence.
The price of the pizza is R31 while a milkshake costs R25.
Submit your answer as: and